Calcifer is a 'fire demon'; your name are similar; Calcifer was a 'falling' star; he does pacts (he asks Howl's heart); Sophie wants him to live for another THOUSAND years.
Nice point, Joao. "Lucifer" means "light-bringer"; it's a personification of the Dayspring, the bright and morning star. It's a kind of historical accident that the name became attached to the fallen archangel, Satan, the Prince of Darkness, in Judao-Christian myth.
So "Calcifer" is the "fire-bringer" - a demon, though probably not a fallen angel. Not sure about the thousand years!
I think the word `Demon` is a bit misused in the translation from the original Japanese and perhaps the term `fire spirit` might be a bit more accurate. Within the film`s dialogue there are plenty of clues that in this world `fire spirits` exist in all types of fire and only exist for as long as the fire burns. They can survive for longer however if they can make a contract with a human sorcerer where they provide greater magical power in return for `life force`. This is symbolised by the sorcerer giving the `spirit` a part of themselves as part of the bargain. In Howl`s case his heart and later Sophie`s braid.
"Any plan that involves losing your hat is a BAD plan.""
A lot of strange things can happen when you translate something from one language to another then somebody else translates a slightly different version back. Particularly when dealing with languages as far apart as English and Japanese. For example Howl`s apprentice Markle has the very ordinary name Michael in the original book. This is because the Japanese tend to pronounce the European name "Michael" something like "Markle" and whoever did the English language translation of the film`s screenplay translated it phonetically.
While in the book Calcifer is referred to as a demon, he`s described as a fire demon and not as anything specifically from Christian mythology, just a creature of semi-supernatural origin from that world, which isn`t ours. Just how that idea translates from English to Japanese then back again with all the different cultural differences involved is inevitably going to be complicated.
"Any plan that involves losing your hat is a BAD plan.""